Third-placed Arsenal led 2-0 after 35 minutes but were rocked by a ferocious West Ham fightback and although they scrambled a point thanks to Laurent Koscielny, their Premier League title hopes look all but over.
They are now 10 points behind leaders Leicester, who play away to Sunderland on Sunday, with six matches left.
"Do we still have an opportunity to win the title? I don't know," Arsenal manager Arsene Wenger said. "We made it more difficult today."
Arsenal had an early let-off when Manuel Lanzini's goal was wrongly disallowed for offside and took advantage when Mesut Ozil fired home from Alex Iwobi's astute pass.
Alexis Sanchez finished off a slick passing move to make it 2-0 to the Gunners after 35 minutes.
Undaunted, West Ham were level before the break thanks to a devastating burst from Carroll.
First he met Aaron Cresswell's cross with a thumping header which gave David Ospina no chance and then in stoppage-time he acrobatically volleyed into the corner.
West Ham swarmed forward at the start of the second half, having a Dimitri Payet effort ruled out before Carroll headed in Michail Antonio's cross.
Nacho Monreal's shot was hacked off the line by Lanzini but Arsenal levelled after 70 minutes when some intricate passing ended with Danny Welbeck flicking the ball to Koscielny who stabbed a shot high past Adrian.
Sanchez could have won it for Arsenal while the superb Payet reduced Arsenal's defence to nervous jitters but neither side could claim maximum points.
"It was a great game of football, magnificent," West Ham manager Slaven Bilic, whose side equalled a club record with a 14th successive home game without defeat, said.
However, their hopes of celebrating their move to the Olympic Stadium after more than a century at Upton Park by qualifying for the Champions League are receding after three consecutive draws.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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